1. Technical Field
Methods and systems disclosed herein are directed to identifying edge pixels in images using fractal signatures.
2. Background
Edge detection is a feature detection and extraction process used in image and graphics processing. An edge is a relatively sharp change in an image property, such as luminosity, that may be associated with an event or change in a property of the image, such as a discontinuity in depth, a discontinuity in depth surface orientation, changes in material properties, and variations in scene illumination. For example, grey levels in a digital image tend to be relatively consistent across a homogeneous region associated with an image object, and inconsistent along a boundary or edge between regions associated with different image objects. Inage pixels along such a boundary are referred to as edge pixels.
Conventional methods of edge detection include search-based edge detection and zero-crossing based edge detection. Search-based methods detect edges by first computing a measure of edge strength, usually a first-order derivative expression such as a gradient magnitude, and then searching for local directional maxima of the gradient magnitude using a computed estimate of the local orientation of the edge, usually the gradient direction. Search-based, or first-order derivative methods include a Canny edge detector, a Canny-Deriche detector, a Sobel operator, and a Robert's Cross operator. Zero-crossing based methods of edge detection search for zero crossings in a second-order derivative expression computed from the image, usually the zero-crossings of a Laplacian or of a non-linear differential expression. Zero-crossing or second-order derivative edge detection methods include a Marr-Hildreth operator.
In fractal geometry, a fractal dimension is a statistical quantity indicative of how completely a fractal appears to fill space on various scales. The term “fractal” was coined by Benoît Mandelbrot, who defined a fractal as a rough or fragmented geometric shape that can be subdivided into parts, each of which is, at least approximately, a reduced-size copy of the whole. Fractal dimensions include a Hausdorff dimension, a packing dimension, Rényi dimensions, a box-counting dimension, and a correlation dimension.
A fractal dimension may be a real number, including but not limited to an integer. For example, the fractal dimension of a plane may range from 2.0 to 3.0, where a perfectly smooth plane has a fractal dimension of 2.0, and an irregular plane may have fractal dimension approaching or equal to 3.0. Whereas in Euclidean geometry, geometric shapes are assigned integer dimension values that are independent of the size of the geometric shapes. For example, in Euclidean geometry, the dimension of a point is zero (0), the dimension of a curve is one (1), the dimension of a plane is two (2), and the dimension of a cube is three (3).
In the drawings, the leftmost digit(s) of a reference number identifies the drawing in which the reference number first appears.